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. Author manuscript; available in PMC: 2012 May 9.
Published in final edited form as: IEEE Int Conf Robot Autom. 2011 May 9:667–673. doi: 10.1109/ICRA.2011.5980311

Fig. 5.

Fig. 5

Parameterization definition: we assume that the entry and exit points x⃗0 and x⃗ t, as well as the direction n⃗0 are defined. For any arbitrarily selected x⃗1 there exists only one circular arc passing through it, so by fixing the location of x⃗1 we fully define the first section (A). Since specifying x⃗i also defines the direction n⃗i for the next section x⃗i + 1, we can recursively specify points x⃗1, …, x⃗N−1, with x⃗N = x⃗t and thus fully define a unique N- sectioned robot (B).